(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A tube of uniform cross-section [itex]A[/itex] is bent to form a circular arc of radius [itex]R[/itex], forming three quarters of a circle. A liquid of density [itex]\rho[/itex] is forced through the tube with a linear speed [itex]v[/itex]. Find the net force exerted by the liquid on the tube.

2. The attempt at a solution

The centripetal force acting on a small element of [itex]dm[/itex] mass will be

[tex]dF=\frac{v^2}{R}dm=\frac{\rho v^2}{R}dV=\frac{\rho A v^2}{R}dl[/tex].

Integrating with proper limits, I got

[tex]F=\frac{\rho A v^2}{R}\int_{0}^{3\pi R/2}dl=\frac{3\pi A \rho v^2}{2}[/tex]

However the answer provided in my book is [itex]\sqrt{2} \rho Av^2[/itex] .What am I doing wrong. Can someone guide me?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Hydrodynamics : Calculate force exerted by fluid on Tube

**Physics Forums | Science Articles, Homework Help, Discussion**